Pressure-Induced Valence Crossover and Novel Metamagnetic Behavior near the Antiferromagnetic Quantum Phase Transition of YbNi$_{3}$Ga$_{9}$

1.6 MB·English

by  K. Matsubayashi

Pressure-Induced Valence Crossover and Novel Metamagnetic Behavior near the
Antiferromagnetic Quantum Phase Transition of YbNi Ga
3 9
K. Matsubayashi,1,∗ T. Hirayama,1 T. Yamashita,2 S. Ohara,2 N. Kawamura,3
M. Mizumaki,3 N. Ishimatsu,4 S. Watanabe,5 K. Kitagawa,6 and Y. Uwatoko1
1Institute for Solid State Physics, The University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8581, Japan
2Department of Engineering Physics, Electronics and Mechanics,
Graduate School of Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan
3Japan Synchrotron Radiation Research Institute (JASRI/SPring-8), 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan
4Department of Physical Science, Graduate School of Science, Hiroshima University,
5
1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526, Japan
1
5Quantum Physics Section, Kyushu Institute of Technology, Fukuoka 804-8550, Japan
0
6Graduate School of Integrated Arts and Sciences, Kochi University, Kochi 780-8520, Japan
2
(Dated: January 29, 2015)

n
a Wereportelectricalresistivity,acmagneticsusceptibilityandX-rayabsorptionspectroscopymea-
J surements of intermediate valence YbNi3Ga9 under pressure and magnetic field. We have revealed

8 a characteristic pressure-induced Yb valence crossover within the temperature-pressure phase di-
2 agram, and a first-order metamagnetic transition is found below Pc ∼ 9 GPa where the system
undergoes a pressure-induced antiferromagnetic transition. As a possible origin of the metamag-

] neticbehavior,acriticalvalencefluctuationemergingnearthecriticalpointofthefirst-ordervalence
l
e transition is discussed on thebasis of the temperature-field-pressurephasediagram.
-
r
t
s In heavy fermion compounds, tuning the ground state the application of pressure [13, 14]. In the vicinity of
.
t by pressure and/or magnetic field from a non-magnetic themagneticQCP,novelmetamagneticbehaviorisoften
a
m state to a magnetic state or vice versa has attracted at- observed in the paramagnetic regime [15, 16], possibly
tention because the anomalous behavior, such as uncon- related to a change of Fermi surface or valence instabil-
-
d ventional superconductivity or non-Fermi liquid (NFL) ity. Therefore,it is naturalto raisethe questionhow the
n state, appears in the vicinity of quantum critical point metamagnetic transition as well as the Yb valence state
o
(QCP) where a second order magnetic phase transition evolveapproachingtoamagneticQCP.However,experi-
c
is suppressed to T = 0 K [1, 2]. The conventional spin mentalcomplicationsincombinationwith highpressure,
[
fluctuationtheoriesreproducetheNFLbehaviorinmany magnetic field and low temperature make it challenging.
1
cases [3–5], however, recent studies, especially on Yb-
v In this Letter, we report a comprehensive study on
based heavy fermion compounds such as YbRh Si , β-
3 2 2 intermediate valence YbNi Ga using both hydrostatic
7 YbAlB4 and Yb15Al34Au51, revealed that these systems pressure and magnetic fiel3d as9 tuning parameter, and
9 exhibit anomalous quantum critical behavior deviating
present the precise temperature-magnetic field-pressure
6 from the conventional QCP scenario and the common
0 (T-H-P) phase diagram in the vicinity of the pressure-
low-temperatureexponentsofthephysicalpropertiesare
. induced antiferromagnetic (AFM) transition together
1 observed[6–8]. Inparticular,anintriguingmysteryisan
with the pressure variation of the Yb valence state.
0 enhanced uniform magnetic susceptibility, giving rise to
5 alargeWilsonratioinspiteoftheabsenceofaferromag- YbNi3Ga9 crystallizes in the ErNi3Al9-type layered
1 structure [17]. In this structure, Yb-ions are in Yb Ga -
neticphasenearby. Toelucidatethenatureoftheuncon- 2 3
v: layerseparatedbysevennonmagnetictriangular-layersof
ventional critical behavior and the underlying physics, a
i Ga or Ni-ions and form a two-dimensional honeycomb-
X number of theories have been proposed such as the local
lattice [18–20]. At ambient pressure, YbNi Ga shows
criticality theory based on the Kondo breakdown QCP, 3 9
r
valence fluctuation behavior with a Kondo temperature
a the theory of the tricritical point and the theory of the
T of 570 K. In contrast to the paramagnetic magnetic
QCP of valence transition [9–12]. Although these theo- K
ground state in YbNi Ga , the isostructural YbNi Al
riespredictsomeimportantaspectsacrosstheQCPsuch 3 9 3 9
exhibits a helical magnetic order at T ∼ 3.4 K with
asajumpintheFermisurfacevolumeoracriticalvalence M
the propagation vector k = (0, 0, 0.8) [20–23]. Recent
fluctuation, the nature of the unconventional criticality
X-ray photoemission spectroscopy reported that the Yb
still remains an open question.
valence states of YbNi Ga and YbNi Al at low tem-
3 9 3 9
Whereas most of the detailed investigations were car- perature were estimated to be 2.43 and 2.97, respec-
riedoutbytuningmagneticfield,anotherimportantclue tively [24]. Therefore, high-pressure study on YbNi Ga
3 9
astothenatureofthequantumcriticalityhascomefrom is expected to cross a magnetic QCP because applying
high-pressure studies. In ytterbium (Yb) systems, it is pressure favors the magnetic Yb3+ configuration with
well known that the evolution of magnetism from non- a smaller volume. Here we demonstrate that the re-
magnetic Yb2+ to magnetic Yb3+ is achieved through alization of the pressure-induced valence crossover and
2
(a) (b)3.0
2 11 K Yb2+ 16.1 GPa 7.0
329 K 14.5 4.9
1 Yb3+ 1110..52 31..63
0 GPa 7.7 0 GPa
0
2 11 K 2.9
300 K
1
XAS (arb. units)22100 131404 0 KK K 37..60 GGPPaa Yb valence state 2.8
300 K 2.7
1
10.2 GPa
0
2 11 K
300 K 2.6
1
YbNiGa
14.5 GPa 3 9
0
8.92 8.94 8.96 8.98 1 10 100
E (keV) T (K)
FIG. 2. (Color online) (a) XAS spectra of YbNi3Ga9 at se-
lected pressures and temperatures for the Yb L3-edge. (b)
Temperature dependence of the averaged valence for various
pressures.
Japan [27]. The sample was loaded in a diamond anvil
FIG. 1. (Color online) (a) Temperature dependence of ρmag cell (DAC) together with ruby chips, which served as
of YbNi3Ga9 under various pressures. The inset shows T-
′ a pressure manometer. Nano-polycristalline diamond
dependenceofχ atvariouspressures.Thedistinctanomalies
ac
′ (NPD) anvils were used to avoid glitches in XAS spec-
asmarkedbyarrowsatTN inρmag andχac correspondtothe
AFM transition. (b) ρmag as a function of T2 at selected tra [28, 29]. The X-ray wave vector was aligned parallel
pressure. The inset shows the low temperature ρmag at 9.0 to the c-axis. In the above high-pressure experiments,
GPainalinearscale. (c)Thelog-logplotofAcoefficientand the pressure-transmitting mediums for the ac magnetic
Tmax. The broken line indicates A ∝ Tm−a2x. susceptibility and the others (resistivity and XAS) were
argon and glycerin, respectively.
Figure 1 shows the temperature dependence of the
the metamagnetic behavior in YbNi3Ga9 near the AFM magnetic part of the electrical resistivity (ρmag) of
quantum phase transition, which suggests the relevance YbNi Ga at selected pressures. Here, ρ is obtained
3 9 mag
of the valence instability for the quantumcriticalbehav- by subtracting the resistivity of the isostructural non-
ior in heavy fermion systems. magneticcompoundLuNi Ga [20,30]. Atambientpres-
3 9
Single crystals of YbNi3Ga9 were grown by a Ga self- sure,ρmagexhibitsabroadpeakcenteredataroundroom
flux method as described previously [19, 20]. The resid- temperature. Application of pressure enhances the mag-
ual resistivity ratio is 460, reflecting the high quality of nitude of the ρmag and the maximum temperature of
thesinglecrystals. Electricalresistivitywasmeasuredby Tmax for ρmag shifts to lower temperature. At pressures
a standard four-probe technique with current flow along above ∼9.5 GPa, the pressure dependence of Tmax tends
the a-axis using a cubic anvil cell, in which highly hy- tobesaturatedandanewresistiveanomalyabruptlyap-
drostatic pressure is realized owing to the multiple-anvil pearsatTN ∼3K,whichbecomesmorepronouncedand
geometry [25]. The ac magnetic susceptibility was mea- shiftstohighertemperaturewithincreasingpressure. As
sured by a conventional mutual-inductance technique at shown in the inset of Fig. 1, ac magnetic susceptibility
a fixed frequency of 317 Hz with a modulation field of experimentsshowedaclearcuspatalmostthesametem-
0.1 mT applied along the a-axis. A newly developed perature as that of the resistive anomaly, indicating the
opposed-anvil pressure cell with was used for ac sus- AFM transition at pressures exceeding Pc ∼ 9.0 GPa.
ceptibility measurements [26]. The applied pressure was Pressure variation of the low temperature resistivity
calibrated by the pressure dependence of the supercon- toward the P was analyzed in terms of Fermi-liquid be-
c
ductingtransitiontemperatureoflead. X-rayabsorption havior: ρ=ρ +AT2atT ≤T . AsshowninFig.1(b),
0 FL
(XAS) measurements at the Yb L -edge were performed the A-value is strongly enhanced and T shifts to the
3 FL
under pressure at the beamline BL39XU of SPring-8, lowertemperatureswithincreasingpressure,whereasthe
3
temperature dependence changesfromthe T2 to alinear
ibsncesahelaetvoiinofrFFiinigg.t.h11(e(bcv))i)c..inNAitesyxstuo,mfwPinecgp(sltoehetedATatvasaTtms9caa.x0leiGsnPwaailtoihng-ttlhhogee (a)s) 22..57 K χ ′ (arb. units) T = 0.4 K (s)b) 000 ..T36 P = 8.5 GPa
rtKheoleantadifooonrtseehmmipepn.etHrioaontwueerdevreTerl,Kaw,tieAono,ibsssueexrgvgpeeescattiecmndlgaexatprordefsoesvlulioarwet-ioi∝nndTfurmc−oeam2dx χ ′ (arb. unit 1210....5004 0µ.60H (T0.)8 χ ′ (arb. unit 000...7865 Tcr
crossover from the weakly correlated to strongly corre-
1.0
P = 8.5 GPa H
lated heavy fermion regime due to the valence crossover. m
0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 2 4 6
In order to track the pressure variation of Yb valence µ0H (T) T (K)
sadmiYrntenebaesrFdpatieaiseogY,utcn.trbY∼s2ie3v(bd8a+ea.tla)9Lya.ta4.3rm4vR-eTeaebkdrohfleiigbeoeVeensucerttsXaerinnptvlAaedgremteSditasvhpssieupneeprrriemaneotch,ttmituexertniraehnesdseepsoitnvfeLayatcnY3ltopedrbtfnearpNactareakhine3secssaGhisattYuaai∼orrbw9ean28eshc+sa.taa9koevs5crfe0ossoYhmhbkfoobeeptwu2Vheo+lnne--, (c)χ ′ (arb. units) 222112......645080 K χ ′ (arb. units) T 0=µ.6 00H.4 ( T0K.)8 χ ′ ((arb. units)d) 0000. ..6T565 TN
0.4
nent to that of Yb3+ component increases with lowering P = 9.1 GPa H 0.8 P = 9.1 GPa
m
temperature. Withincreasingpressure,thistemperature 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 1 2 3 4 5
variation of the Yb valence state becomes weaker and µ0H (T) T (K)
the spectral weight transfers from Yb2+ to Yb3+ state.
TheaveragedvalencewasdeterminedbyfittingtheXAS
spectra to an arctangent step function and a Lorentzian FIG.3. (Coloronline)Magneticfieldandtemperaturedepen-
′
peak for each valence state (see the Supplemental Ma- dence of χac in YbNi3Ga9 at 8.5 GPa (a), (b) and 9.5 GPa
terial [31]). As shown in Fig. 2(b), Yb valence mono- (c), (d). Curves are shifted for clarity. The upper insets in
′
tonically increases with increasing pressure and reaches (a) and (c) are hysteresis curves of χac(H) measurements at
T = 0.4 K.
a value close to 2.9 at around P where the temperature
c
dependence of Yb valence becomes weak.
To search for the metamagnetic behavior, we focus
on the effect of magnetic field in the vicinity of P . magnetic field is applied along the easy a-axis of mag-
c
The field and temperature dependences of χ′ for dif- netization [20, 22], suggesting that the pressure-induced
ac
AFM phase in YbNi Ga may have the helical magnetic
ferent constant temperatures and fields are displayed 3 9
in Figs. 3(a),(b) and (c),(d) at below and above P structureidenticaltothatofYbNi3Al9,i.e.,theYbmag-
c
(∼9 GPa), respectively. At 8.5 GPa, by application of neticmomentsareferromagneticallyalignedintheplane
magnetic field along the a-axis, we found a first order of Yb2Al3 layers, which has a weak interlayer magnetic
metamagnetic transition in the H-sweep measurements coupling.
at H ∼ 0.69 T with hysteresis at 0.4 K (see the inset The anomalies observed in the temperature and field
m
′
of Fig. 3(a)). With increasing temperature, H slightly scans in χ are summarized in the H-T-P phase dia-
m ac
shifts to lower fields. As the temperature is increased gramofYbNi Ga inFig.5togetherwithacontourplot
3 9
further, the magnitude ofthe anomalystartsto decrease of the Yb valence value in T-P plane. Upon the appli-
and is smeared out. Therefore, the first order metamag- cation of pressure, we can see a clear evolution of the
netic transition becomes a crossover via a critical point Yb-valence toward the magnetic trivalent state as well
(CP). As shown in Fig. 3 (b), the existence of the CP as the change from the nonmagnetic to the magnetic
is also confirmed by the divergent behavior in the tem- ground state. The striking feature of the phase diagram
perature dependence of χ′ at T ∼ 2.1 K by tuning is that T is cut off by a AFM transition temperature
ac cr FL
themagneticfieldtoH ∼H whileχ′ exhibitsabroad T , suggestingthe first-ordernature of this transitionat
m ac N
maximumawayfromH . Moreinterestingly,evenabove P . Interestingly, the valence crossover region ∼2.8 con-
m c
P at 9.1 GPa, a metamagnetic transition occurs from vergestowardP . Thischaracteristicvariationofthe Yb
c c
the AFM to a spin-polarized state at low temperatures valence state in the T-P phase diagram closely resem-
(see Fig. 3(c) and (d)). The low temperature first or- bles that of YbInCu , which is known as a prototypical
4
der metamagnetic transition with a hysteretic behavior compound for the isostructural first-order valence tran-
changes into the second order transition at higher tem- sition(FOVT)betweenthehightemperaturephasewith
peratures throughthe tricriticalpoint (TCP), where the Yb+2.97 and the low temperature phase with Yb+2.84 at
′
distinct cusp in χ becomes sharper and enhanced in ambient pressure. In the case of YbInCu , a first-order
ac 4
field and temperature dependence. This is reminiscent ferromagnetic (FM) order emerges when the FOVT is
of the metamagnetic transition in YbNi Al where the suppressed to lower temperatures by applying pressure.
3 9
4
compoundsunder highmagneticfield[35]. Furthermore,
3.0 recent theoretical calculations for an extended periodic
Anderson model explain that the emergence of FOVT
YbNi Ga 2.9 Y
b or the valence crossover is governed by the Coulomb re-
3 9 v
a
2.8 el pulsionbetweenthef andconductionelectrons,andthus
n
T ec theFOVTisinducedbyapplyingthemagneticfieldeven
max TN 2.7 etats intheintermediate-valencestate,resultingintheappear-
2.6 ance of the metamagnetic behavior [36]. It is worth not-
ing that the enhanced ferromagnetic fluctuations is pre-
100
AFM dicted to develop near the CP of FOVT [12], in accor-
TFL PM 12 dance with our observation of the striking enhancement
T (K) 10 8 10 14 iwneχa′asccrnibeaertthhaetCthPe omfetthaemmagentaetmicagcrnoestsicovleinrea.tTzehreorefifoerlde
6 Pc H 12 evolves into a sharp first-order metamagnetic transition
1 4 m 10 associated with the valence instability under magnetic
2 8 field. We alsospeculatethatthe criticalfluctuationsdue
0.0 0.2 6P (GPa) to the proximity to the valence crossover line extended
0.4 4 fromtheFOVTlineisakeyingredientresponsibleforthe
0.6
μ 0H (T0).8 1.0 2 unconventionalcriticalbehavior,especiallyforthediver-
1.2 genceofuniformsusceptibilityinparamagneticphase,in
other Yb systems such as YbRh Si and β-YbAlB . For
2 2 4
YbNi Ga , the extremely low value of the critical field
3 9
FIG. 4. (Color online) Contour plot of the Yb valence in H implies the closeness to a quantum critical endpoint
m
the temperature-pressure phase diagram of YbNi3Ga9. The (QCEP)oftheFOVT,atwhichdivergingvalencefluctu-
transitionandcrossovertemperaturesarededucedfromresis-
ations could be coupled to the Fermi-surface instability.
tivity (circles) and ac magnetic susceptibility (squares) mea-
It is an important experimental challenge to determine
surements. Here,closed squaresbelow and abovePc indicate
the CP and TCP, respectively. The dashed lines are guides the location of the QCEP and the critical behavior by
to theeye. fine tuning pressure and magnetic field, which deserves
further investigations.
In conclusion, we present the phase diagram of
Despite the difference ofbetween FOVT and the valence
YbNi Ga as a function of pressure, magnetic field and
3 9
crossover,these compounds as well as in other Yb-based
temperature. We identify the clear Yb valence crossover
heavy fermion compounds [32, 33] share similar inter-
toward P of the the pressure-induced AFM transition
c
play between magnetic and valence instabilities. Hence,
and,moreover,afirst-ordermetamagnetictransitionpos-
itislikelythatasuppressionofthe magneticordertakes
sibly due to the valence instability. The resulting phase
place due to enhanced valence fluctuations, giving rise
diagram provides new insights into the unconventional
to the occurrence of the first-order magnetic transition.
quantum critical behavior in heavy fermion systems.
In fact, the slave-boson mean-field calculation demon-
We acknowledge discussions with K. Miyake,
stratesthatacoincidenceofthe AFM transitionandthe
N. K. Sato and N. Mori. We are grateful to H. Sumiya
valencecrossoveratT ∼0Kcouldoccurdependingupon
and T. Irifune for providing the NPD anvils. This work
the strength of the hybridization, causing the first-order
is partially supported by Grants-in-Aid (No.24740220,
AFM transition [34].
24540389)forScientificResearchfromthe JapanSociety
With approaching P from the paramagnetic side,
c for the Promotion of Science, the approval of the Japan
there exists the first-order metamagnetic transition with
Synchrotron Radiation Research Institute (JASRI)
the CP, which seems to merge to the TCP of the AFM
(Proposal No.2011B2097, 2011B2094, 2011B2092,
orderaboveP . HereweconsidertheClausius-Clapeyron
c 2012A1283, 2012A1843, 2012B1976, 2012B0046,
relation for the metamagnetic field H : d(µ H )/dT =
m 0 m 2013A0046), and Grants-in-Aid for Scientific Research
-∆S/∆M,whereM andS denotethemagnetizationand
on Innovative Areas Heavy Electrons (No.20102007)
the entropy, respectively. Since the first order metamag-
fromtheMinistryofEducation,Culture,Sports,Science
neticlinebelowP hasanegativeslopeintheH-T plane,
c and Technology, Japan.
the entropyofthe low-fieldregionissmallerthanthatof
high-field region. One possible interpretation of this re-
sult is that the Yb ion changes from the mixed-valent
nonmagnetic state to the trivalent state with magnetic
degrees of freedom by the application of magnetic field. ∗ [email protected]
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